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<div class="subTitle">org.apache.commons.math3.complex</div>
<h2 title="Class Quaternion" class="title">Class Quaternion</h2>
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<pre>public final class <span class="strong">Quaternion</span>
extends <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>
implements <a href="http://docs.oracle.com/javase/6/docs/api/java/io/Serializable.html?is-external=true" title="class or interface in java.io">Serializable</a></pre>
<div class="block">This class implements <a href="http://mathworld.wolfram.com/Quaternion.html">
 quaternions</a> (Hamilton's hypercomplex numbers).
 <br/>
 Instance of this class are guaranteed to be immutable.</div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>3.1</dd>
<dt><span class="strong">Version:</span></dt>
  <dd>$Id: Quaternion.java 1421249 2012-12-13 12:32:03Z erans $</dd>
<dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../serialized-form.html#org.apache.commons.math3.complex.Quaternion">Serialized Form</a></dd></dl>
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<caption><span>Fields</span><span class="tabEnd">&nbsp;</span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Field and Description</th>
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<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#I">I</a></strong></code>
<div class="block">i</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#IDENTITY">IDENTITY</a></strong></code>
<div class="block">Identity quaternion.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#J">J</a></strong></code>
<div class="block">j</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#K">K</a></strong></code>
<div class="block">k</div>
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<tr class="altColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#ZERO">ZERO</a></strong></code>
<div class="block">Zero quaternion.</div>
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<th class="colOne" scope="col">Constructor and Description</th>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#Quaternion(double[])">Quaternion</a></strong>(double[]&nbsp;v)</code>
<div class="block">Builds a pure quaternion from a vector (assuming that the scalar
 part is zero).</div>
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<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#Quaternion(double, double[])">Quaternion</a></strong>(double&nbsp;scalar,
          double[]&nbsp;v)</code>
<div class="block">Builds a quaternion from scalar and vector parts.</div>
</td>
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<tr class="altColor">
<td class="colOne"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#Quaternion(double, double, double, double)">Quaternion</a></strong>(double&nbsp;a,
          double&nbsp;b,
          double&nbsp;c,
          double&nbsp;d)</code>
<div class="block">Builds a quaternion from its components.</div>
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<th class="colFirst" scope="col">Modifier and Type</th>
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<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#add(org.apache.commons.math3.complex.Quaternion)">add</a></strong>(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q)</code>
<div class="block">Computes the sum of the instance and another quaternion.</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#add(org.apache.commons.math3.complex.Quaternion, org.apache.commons.math3.complex.Quaternion)">add</a></strong>(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q1,
   <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q2)</code>
<div class="block">Computes the sum of two quaternions.</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#dotProduct(org.apache.commons.math3.complex.Quaternion)">dotProduct</a></strong>(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q)</code>
<div class="block">Computes the dot-product of the instance by a quaternion.</div>
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<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#dotProduct(org.apache.commons.math3.complex.Quaternion, org.apache.commons.math3.complex.Quaternion)">dotProduct</a></strong>(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q1,
          <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q2)</code>
<div class="block">Computes the dot-product of two quaternions.</div>
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<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#equals(java.lang.Object)">equals</a></strong>(<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>&nbsp;other)</code></td>
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<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#equals(org.apache.commons.math3.complex.Quaternion, double)">equals</a></strong>(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q,
      double&nbsp;eps)</code>
<div class="block">Checks whether this instance is equal to another quaternion
 within a given tolerance.</div>
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</tr>
<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getConjugate()">getConjugate</a></strong>()</code>
<div class="block">Returns the conjugate quaternion of the instance.</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getInverse()">getInverse</a></strong>()</code>
<div class="block">Returns the inverse of this instance.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getNorm()">getNorm</a></strong>()</code>
<div class="block">Computes the norm of the quaternion.</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getPositivePolarForm()">getPositivePolarForm</a></strong>()</code>
<div class="block">Returns the polar form of the quaternion.</div>
</td>
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<tr class="altColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getQ0()">getQ0</a></strong>()</code>
<div class="block">Gets the first component of the quaternion (scalar part).</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getQ1()">getQ1</a></strong>()</code>
<div class="block">Gets the second component of the quaternion (first component
 of the vector part).</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getQ2()">getQ2</a></strong>()</code>
<div class="block">Gets the third component of the quaternion (second component
 of the vector part).</div>
</td>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getQ3()">getQ3</a></strong>()</code>
<div class="block">Gets the fourth component of the quaternion (third component
 of the vector part).</div>
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<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getScalarPart()">getScalarPart</a></strong>()</code>
<div class="block">Gets the scalar part of the quaternion.</div>
</td>
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<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getVectorPart()">getVectorPart</a></strong>()</code>
<div class="block">Gets the three components of the vector part of the quaternion.</div>
</td>
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<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#hashCode()">hashCode</a></strong>()</code></td>
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<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#isPureQuaternion(double)">isPureQuaternion</a></strong>(double&nbsp;eps)</code>
<div class="block">Checks whether the instance is a pure quaternion within a given
 tolerance.</div>
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<td class="colFirst"><code>boolean</code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#isUnitQuaternion(double)">isUnitQuaternion</a></strong>(double&nbsp;eps)</code>
<div class="block">Checks whether the instance is a unit quaternion within a given
 tolerance.</div>
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<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#multiply(double)">multiply</a></strong>(double&nbsp;alpha)</code>
<div class="block">Multiplies the instance by a scalar.</div>
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<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#multiply(org.apache.commons.math3.complex.Quaternion)">multiply</a></strong>(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q)</code>
<div class="block">Returns the Hamilton product of the instance by a quaternion.</div>
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<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#multiply(org.apache.commons.math3.complex.Quaternion, org.apache.commons.math3.complex.Quaternion)">multiply</a></strong>(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q1,
        <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q2)</code>
<div class="block">Returns the Hamilton product of two quaternions.</div>
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<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#normalize()">normalize</a></strong>()</code>
<div class="block">Computes the normalized quaternion (the versor of the instance).</div>
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<td class="colFirst"><code><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#subtract(org.apache.commons.math3.complex.Quaternion)">subtract</a></strong>(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q)</code>
<div class="block">Subtracts a quaternion from the instance.</div>
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<td class="colFirst"><code>static <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#subtract(org.apache.commons.math3.complex.Quaternion, org.apache.commons.math3.complex.Quaternion)">subtract</a></strong>(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q1,
        <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q2)</code>
<div class="block">Subtracts two quaternions.</div>
</td>
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<td class="colFirst"><code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#toString()">toString</a></strong>()</code></td>
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<code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</a></code></li>
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<h4>IDENTITY</h4>
<pre>public static final&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a> IDENTITY</pre>
<div class="block">Identity quaternion.</div>
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<pre>public static final&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a> ZERO</pre>
<div class="block">Zero quaternion.</div>
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<pre>public static final&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a> I</pre>
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<pre>public static final&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a> J</pre>
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<pre>public static final&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a> K</pre>
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<pre>public&nbsp;Quaternion(double&nbsp;a,
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<div class="block">Builds a quaternion from its components.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - Scalar component.</dd><dd><code>b</code> - First vector component.</dd><dd><code>c</code> - Second vector component.</dd><dd><code>d</code> - Third vector component.</dd></dl>
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<pre>public&nbsp;Quaternion(double&nbsp;scalar,
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<div class="block">Builds a quaternion from scalar and vector parts.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>scalar</code> - Scalar part of the quaternion.</dd><dd><code>v</code> - Components of the vector part of the quaternion.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the array length is not 3.</dd></dl>
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<pre>public&nbsp;Quaternion(double[]&nbsp;v)</pre>
<div class="block">Builds a pure quaternion from a vector (assuming that the scalar
 part is zero).</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>v</code> - Components of the vector part of the pure quaternion.</dd></dl>
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;getConjugate()</pre>
<div class="block">Returns the conjugate quaternion of the instance.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the conjugate quaternion</dd></dl>
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<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;multiply(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q1,
                  <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q2)</pre>
<div class="block">Returns the Hamilton product of two quaternions.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>q1</code> - First quaternion.</dd><dd><code>q2</code> - Second quaternion.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the product <code>q1</code> and <code>q2</code>, in that order.</dd></dl>
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;multiply(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q)</pre>
<div class="block">Returns the Hamilton product of the instance by a quaternion.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>q</code> - Quaternion.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the product of this instance with <code>q</code>, in that order.</dd></dl>
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<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;add(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q1,
             <a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q2)</pre>
<div class="block">Computes the sum of two quaternions.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>q1</code> - Quaternion.</dd><dd><code>q2</code> - Quaternion.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the sum of <code>q1</code> and <code>q2</code>.</dd></dl>
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;add(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q)</pre>
<div class="block">Computes the sum of the instance and another quaternion.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>q</code> - Quaternion.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the sum of this instance and <code>q</code></dd></dl>
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<pre>public static&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;subtract(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q1,
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<div class="block">Subtracts two quaternions.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>q1</code> - First Quaternion.</dd><dd><code>q2</code> - Second quaternion.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the difference between <code>q1</code> and <code>q2</code>.</dd></dl>
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;subtract(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q)</pre>
<div class="block">Subtracts a quaternion from the instance.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>q</code> - Quaternion.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the difference between this instance and <code>q</code>.</dd></dl>
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<pre>public static&nbsp;double&nbsp;dotProduct(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q1,
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<div class="block">Computes the dot-product of two quaternions.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>q1</code> - Quaternion.</dd><dd><code>q2</code> - Quaternion.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the dot product of <code>q1</code> and <code>q2</code>.</dd></dl>
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<pre>public&nbsp;double&nbsp;dotProduct(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q)</pre>
<div class="block">Computes the dot-product of the instance by a quaternion.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>q</code> - Quaternion.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the dot product of this instance and <code>q</code>.</dd></dl>
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<pre>public&nbsp;double&nbsp;getNorm()</pre>
<div class="block">Computes the norm of the quaternion.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the norm.</dd></dl>
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;normalize()</pre>
<div class="block">Computes the normalized quaternion (the versor of the instance).
 The norm of the quaternion must not be zero.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>a normalized quaternion.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></code> - if the norm of the quaternion is zero.</dd></dl>
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<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a></code>&nbsp;in class&nbsp;<code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></code></dd>
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<pre>public&nbsp;boolean&nbsp;equals(<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;q,
             double&nbsp;eps)</pre>
<div class="block">Checks whether this instance is equal to another quaternion
 within a given tolerance.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>q</code> - Quaternion with which to compare the current quaternion.</dd><dd><code>eps</code> - Tolerance.</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>true</code> if the each of the components are equal
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<pre>public&nbsp;boolean&nbsp;isUnitQuaternion(double&nbsp;eps)</pre>
<div class="block">Checks whether the instance is a unit quaternion within a given
 tolerance.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>eps</code> - Tolerance (absolute error).</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>true</code> if the norm is 1 within the given tolerance,
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<pre>public&nbsp;boolean&nbsp;isPureQuaternion(double&nbsp;eps)</pre>
<div class="block">Checks whether the instance is a pure quaternion within a given
 tolerance.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>eps</code> - Tolerance (absolute error).</dd>
<dt><span class="strong">Returns:</span></dt><dd><code>true</code> if the scalar part of the quaternion is zero.</dd></dl>
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;getPositivePolarForm()</pre>
<div class="block">Returns the polar form of the quaternion.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the unit quaternion with positive scalar part.</dd></dl>
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;getInverse()</pre>
<div class="block">Returns the inverse of this instance.
 The norm of the quaternion must not be zero.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the inverse.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../org/apache/commons/math3/exception/ZeroException.html" title="class in org.apache.commons.math3.exception">ZeroException</a></code> - if the norm (squared) of the quaternion is zero.</dd></dl>
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<pre>public&nbsp;double&nbsp;getQ0()</pre>
<div class="block">Gets the first component of the quaternion (scalar part).</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the scalar part.</dd></dl>
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<pre>public&nbsp;double&nbsp;getQ1()</pre>
<div class="block">Gets the second component of the quaternion (first component
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<dl><dt><span class="strong">Returns:</span></dt><dd>the first component of the vector part.</dd></dl>
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<pre>public&nbsp;double&nbsp;getQ2()</pre>
<div class="block">Gets the third component of the quaternion (second component
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<dl><dt><span class="strong">Returns:</span></dt><dd>the second component of the vector part.</dd></dl>
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<pre>public&nbsp;double&nbsp;getQ3()</pre>
<div class="block">Gets the fourth component of the quaternion (third component
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<dl><dt><span class="strong">Returns:</span></dt><dd>the third component of the vector part.</dd></dl>
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<pre>public&nbsp;double&nbsp;getScalarPart()</pre>
<div class="block">Gets the scalar part of the quaternion.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the scalar part.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getQ0()"><code>getQ0()</code></a></dd></dl>
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<pre>public&nbsp;double[]&nbsp;getVectorPart()</pre>
<div class="block">Gets the three components of the vector part of the quaternion.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the vector part.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getQ1()"><code>getQ1()</code></a>, 
<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html#getQ2()"><code>getQ2()</code></a>, 
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<pre>public&nbsp;<a href="../../../../../org/apache/commons/math3/complex/Quaternion.html" title="class in org.apache.commons.math3.complex">Quaternion</a>&nbsp;multiply(double&nbsp;alpha)</pre>
<div class="block">Multiplies the instance by a scalar.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>alpha</code> - Scalar factor.</dd>
<dt><span class="strong">Returns:</span></dt><dd>a scaled quaternion.</dd></dl>
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<pre>public&nbsp;<a href="http://docs.oracle.com/javase/6/docs/api/java/lang/String.html?is-external=true" title="class or interface in java.lang">String</a>&nbsp;toString()</pre>
<dl>
<dt><strong>Overrides:</strong></dt>
<dd><code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a></code>&nbsp;in class&nbsp;<code><a href="http://docs.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></code></dd>
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